1. Field of the Invention
The present invention relates to an exposure method and a storage medium.
2. Description of the Related Art
An exposure apparatus is employed to fabricate a semiconductor device using a photolithography technique. The exposure apparatus projects and transfers the pattern of a mask (reticle) onto a substrate (for example, a wafer) by a projection optical system.
The exposure apparatus must transfer the pattern of the mask to a desired position in a desired shape. However, it is often the case that several error factors are present in exposure, and this leads to transfer of the pattern of the mask to a position different from a desired position in a shape different from a desired shape. Examples of the error factors include the amount of exposure and the focus position in exposing the substrate to light. Aberrations generated in the projection optical system can also be regarded as one type of error factors. Although the projection optical system includes a mechanism for correcting (controlling) the aberrations, this mechanism has a limited correction capability. Therefore, the projection optical system generally has residual aberrations. Note that the amount of residual aberration and the amount of fluctuation in aberration during exposure (that is, the amount of fluctuation in residual aberration due, for example, to generation of exposure heat) vary in each individual exposure apparatus.
With the recent advances in micropatterning of semiconductor devices, the edge positions of the optical image of the pattern on the substrate must precisely be controlled especially when the pattern of a mask used for a well process of an SRAM memory cell is to be transferred. However, if the projection optical system has aberrations typified by coma aberrations, the edge positions of the optical image significantly fluctuate (shift). Also, as described above, the aberrations of the projection optical system do not stay constant (that is, they fluctuate), and their magnitude also varies in each individual exposure apparatus. Hence, a demand has arisen for a technique of optimizing (determining) the effective light source (the light intensity distribution on the pupil plane of the illumination optical system) so that the pattern of the mask can be transferred with high accuracy even if the projection optical system has aberrations. Note that Japanese Patent No. 4378266 and No. 4319560 propose techniques of optimizing the effective light source.
Unfortunately, although the technique disclosed in Japanese Patent No. 4378266 determines an effective light source which maximizes the margin of the amount of exposure and the margin of the focus position upon defining the edge positions of the optical image of the pattern, it does not take into consideration aberrations existing in the projection optical system. As described above, the aberrations of the projection optical system always exist and fluctuate, and the optical image of the pattern synchronously fluctuates as well. The technique disclosed in Japanese Patent No. 4378266 does not take such influence into consideration at all, so it is impractical to apply this technique to an actual exposure apparatus.
Also, the technique disclosed in Japanese Patent No. 4319560 calculates the response characteristics of the image performance of the optical image to a specific aberration which is generated in each light source obtained by dividing the pupil plane of the illumination optical system, thereby determining an effective light source so that the response characteristics of the image performance to this aberration become poor. However, the technique disclosed in Japanese Patent No. 4319560 does not take into consideration control of the edge positions of the optical image, and therefore does not determine an effective light source which reduces the fluctuation in edge position of the optical image due to a specific aberration. In addition, the technique disclosed in Japanese Patent No. 4319560 does not guarantee a given image performance of the optical image against an unknown aberration, and therefore cannot cope with a situation in which a plurality of exposure apparatuses commonly use the same effective light source or that in which aberrations remain behind or fluctuate.